Multilevel power converters have drawn a lot of attention recently [1], [2]. The modulation technique used in multilevel converters must have high efficiency, reduced passive filter cost, and fast transient response under different dynamic conditions [2], [3]. High efficiency is a critical metric for multilevel converters. Because low switching frequencies lead to low switching power losses, low switching frequency modulation techniques such as selective harmonic elimination-PWM (SHE-PWM) [4], selective harmonic mitigation-PWM (SHM-PWM) [5], and selective harmonic current mitigation-PWM (SHCM-PWM) [6] are promising to increase converter efficiencies. In conventional SHE-PWM or SHM-PWM techniques, only the low order harmonics are eliminated or mitigated to meet voltage harmonic limits [3]. Hence, the conventional SHE-PWM and SHM-PWM techniques cannot ensure that current harmonic limits are met, and these limits are more important than the voltage harmonic limits for the grid tied converters [6]. In addition, the grid voltage harmonics can lead to unmitigated current harmonics for SHE-PWM and SHM-PWM techniques, but this information is not included in the equations of these modulation techniques.
These two problems can be considered by introducing a SHCM-PWM technique [6] that can meet the current harmonic limits of IEEE-519 [11] by including the effects of the grid voltage harmonics in the optimization process. In this technique, the coupling inductance between the converter and the grid can be significantly reduced in comparison to SHE-PWM and SHM-PWM techniques [6]. Moreover, a higher number of current harmonics than SHE-PWM and SHM-PWM techniques can be mitigated with the same number of switching transitions [6]. In He et al. [3], based on the dynamic equations of the grid-tied converters, a high performance dynamic response can be achieved for a four-quadrant grid-tied converter. In addition, an indirect controller is used to change the active and reactive currents four times in each fundamental cycle. The modulation technique used in He et al. is phase-shift PWM (PSPWM), which uses a high switching frequency to control low order harmonics. It is important to note that the SHCM-PWM technique could not be used with the indirect controller technique to obtain high dynamic performance. Because SHCM-PWM is an offline modulation technique and the switching angles are calculated and stored in look-up tables, it needs to use fast Fourier transform (FFT), which results in time delays, to apply switching angles to the converters. In addition, the number of switching transitions is very low in SHCM-PWM, so it results in high ripple currents. As a result, it can cause intrinsic weak dynamic performance [7]. When active or reactive power are controlled with SHCM-PWM in four-quadrant converters, because the switching angles need one fundamental cycle to get updated [7], a DC offset remains on the injected currents for several cycles under dynamic conditions [3].